Related papers: The cavity method: from exact solutions to algorit…
Genetic algorithms, computer programs that simulate natural evolution, are increasingly applied across many disciplines. They have been used to solve various optimisation problems from neural network architecture search to strategic games,…
The second moment method has always been an effective tool to lower bound the satisfiability threshold of many random constraint satisfaction problems. However, the calculation is usually hard to carry out and as a result, only some loose…
Optimization models with non-convex constraints arise in many tasks in machine learning, e.g., learning with fairness constraints or Neyman-Pearson classification with non-convex loss. Although many efficient methods have been developed…
The $XY$ model with four-body quenched disordered interactions and its discrete $p$-clock proxy is studied on bipartite random graphs by means of the cavity method. The phase diagrams are determined from the ordered case to the spin-glass…
We consider the matrix completion problem where the aim is to esti-mate a large data matrix for which only a relatively small random subset of its entries is observed. Quite popular approaches to matrix completion problem are iterative…
A method is suggested for treating those complicated physical problems for which exact solutions are not known but a few approximation terms of a calculational algorithm can be derived. The method permits one to answer the following rather…
This paper considers the computer model calibration problem and provides a general frequentist solution. Under the proposed framework, the data model is semi-parametric with a nonparametric discrepancy function which accounts for any…
We propose finitely convergent methods for solving convex feasibility problems defined over a possibly infinite pool of constraints. Following other works in this area, we assume that the interior of the solution set is nonempty and that…
Coordinate descent algorithms solve optimization problems by successively performing approximate minimization along coordinate directions or coordinate hyperplanes. They have been used in applications for many years, and their popularity…
Compact representations of objects is a common concept in computer science. Automated planning can be viewed as a case of this concept: a planning instance is a compact implicit representation of a graph and the problem is to find a path (a…
This paper studies the distributed optimization problem with possibly nonidentical local constraints, where its global objective function is composed of $N$ convex functions. The aim is to solve the considered optimization problem in a…
Random constraint satisfaction problems undergo several phase transitions as the ratio between the number of constraints and the number of variables is varied. When this ratio exceeds the satisfiability threshold no more solutions exist;…
Many real world problems naturally appear as constraints satisfaction problems (CSP), for which very efficient algorithms are known. Most of these involve the combination of two techniques: some direct propagation of constraints between…
Three aspects of applying homotopy continuation, which is commonly used to solve parameterized systems of polynomial equations, are investigated. First, for parameterized systems which are homogeneous, we investigate options for performing…
Recent research indicates that many convex optimization problems with random constraints exhibit a phase transition as the number of constraints increases. For example, this phenomenon emerges in the $\ell_1$ minimization method for…
Convex optimization problems arising in applications often have favorable objective functions and complicated constraints, thereby precluding first-order methods from being immediately applicable. We describe an approach that exchanges the…
The Promise Constraint Satisfaction Problem (PCSP for short) is a generalization of the well-studied Constraint Satisfaction Problem (CSP). The PCSP has its roots in such classic problems as the Approximate Graph Coloring and the…
We introduce a general class of algorithms and supply a number of general results useful for analysing these algorithms when applied to regular graphs of large girth. As a result, we can transfer a number of results proved for random…
In this paper we present efficient algorithmic solutions for several constrained resource allocation, management and discovery problems. We consider new types of resource allocation models and constraints, and we present new geometric…
Realizing when a model is right for a wrong reason is not trivial and requires a significant effort by model developers. In some cases an input salience method, which highlights the most important parts of the input, may reveal problematic…